The ponding problem on elastic membranes: An analog equation solution

Katsikadelis, JT; Nerantzaki, MS

dc.contributor.author	Katsikadelis, JT	en
dc.contributor.author	Nerantzaki, MS	en
dc.date.accessioned	2014-03-01T01:18:26Z
dc.date.available	2014-03-01T01:18:26Z
dc.date.issued	2002	en
dc.identifier.issn	0178-7675	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/15001
dc.subject	Boundary Condition	en
dc.subject	Equilibrium State	en
dc.subject	Integral Representation	en
dc.subject	Nonlinear Equation	en
dc.subject	Nonlinear Response	en
dc.subject.classification	Mathematics, Interdisciplinary Applications	en
dc.subject.classification	Mechanics	en
dc.subject.other	Boundary conditions	en
dc.subject.other	Boundary element method	en
dc.subject.other	Kinematics	en
dc.subject.other	Membranes	en
dc.subject.other	Nonlinear equations	en
dc.subject.other	Poisson equation	en
dc.subject.other	Ponding	en
dc.subject.other	Prestressing	en
dc.subject.other	Elastic membranes	en
dc.subject.other	Elasticity	en
dc.title	The ponding problem on elastic membranes: An analog equation solution	en
heal.type	journalArticle	en
heal.identifier.primary	10.1007/s00466-001-0275-x	en
heal.identifier.secondary	http://dx.doi.org/10.1007/s00466-001-0275-x	en
heal.language	English	en
heal.publicationDate	2002	en
heal.abstract	In this paper, the nonlinear response of elastic membranes with arbitrary shape under partial and full ponding loads has been analyzed. Large deflections are considered, which result from nonlinear kinematic relations. The problem is formulated in terms of the displacements components and the three coupled nonlinear governing equations are solved using the analog equation method (AEM). The membrane may be prestressed either by prescribed boundary displacements or tractions. Using the concept of the analog equation the three coupled nonlinear equations are replaced by three uncoupled Poisson's equations with fictitious sources under the same boundary conditions. Subsequently, the fictitious sources are established using a procedure based on the BEM and the displacement components as well as the stress resultants at any point of the membrane are evaluated from their integral representations. In addition to the geometrical nonlinearity, the ponding problem is itself nonlinear, because the ponding load depends on the deflection surface that it produces. Iterative schemes are developed which converge to the equilibrium state of the membrane under the ponding loads. Several membranes are analyzed which illustrate the method and demonstrate its efficiency and accuracy. The method has all the advantages of the pure BEM, since the discretization and integration is limited only to the boundary.	en
heal.publisher	SPRINGER-VERLAG	en
heal.journalName	Computational Mechanics	en
dc.identifier.doi	10.1007/s00466-001-0275-x	en
dc.identifier.isi	ISI:000174961100003	en
dc.identifier.volume	28	en
dc.identifier.issue	2	en
dc.identifier.spage	122	en
dc.identifier.epage	128	en